Atomic units (au) form a system of units convenient for electromagnetism, atomic physics, and quantum electrodynamics, especially when the focus is on the properties of electrons. au are designed so that the numerical values of the following six physical constants are all unity by definition: In physics and metrology, units are standards for measurement of physical quantities that need clear definitions to be useful. ... Electromagnetism is the physics of the electromagnetic field: a field, encompassing all of space, which exerts a force on those particles that possess the property of electric charge, and is in turn affected by the presence and motion of such particles. ... Atomic physics (or atom physics) is the field of physics that studies atoms as isolated systems comprised of electrons and an atomic nucleus. ... Quantum electrodynamics (QED) is a relativistic quantum field theory of electromagnetism. ... Properties The electron is a lightweight fundamental subatomic particle that carries a negative electric charge. ... In science, a physical constant is a physical quantity whose numerical value does not change. ...

• Two properties of the electron, its mass and charge;
• Two properties of the hydrogen atom, its Bohr radius and the absolute value of its electric potential energy in the ground state;
• Two constants, Dirac's and that for Coulomb's Law.

Properties The electron is a lightweight fundamental subatomic particle that carries a negative electric charge. ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ... The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ... A hydrogen atom is an atom of the chemical element hydrogen. ... In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. ... In mathematics, the absolute value (or modulus1) of a real number is its numerical value without regard to its sign. ... The electric potential energy of a body is its potential energy due to electric effects, neglecting other forces (such as gravity). ... In physics, the ground state of a quantum mechanical system is its lowest-energy state. ... In science, a physical constant is a physical quantity whose numerical value does not change. ... Plancks constant, denoted h, is a physical constant that is used to describe the sizes of quanta. ... In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ...

Fundamental units

Fundamental Atomic Units
Quantity	Name	Symbol	SI Equivalent	Planck unit
length	Bohr radius	a0	5.291 772 108(18)×10-11 m	10-35 m
mass	electron rest mass	me	9.109 3826(16)×10-31 kg	10-8 kg
charge	elementary charge	e	1.602 176 53(14)×10-19 C	10-18 C
electrostatic force	Coulomb force constant	1/(4πε0)	8.9875516×109 C-2 N m2	1
angular momentum	Dirac constant		1.054 571 68(18)×10-34 J s	1
energy	Hartree energy	Eh	4.359 744 17(75)×10-18 J	109 J

The normalizations of the Coulomb force constant and the Hartree energy are only an incidental consequence of normalizing the other four quantities. The six quantities are not independent; to normalize all six quantities to 1, it suffices to normalize any four of them to 1. Cover of brochure The International System of Units. ... // In physics, Planck units are physical units of measurement originally proposed by Max Planck. ... In general English usage, length (symbols: l, L) is but one particular instance of distance – an objects length is how long the object is – but in the physical sciences and engineering, the word length is in some contexts used synonymously with distance. Height is vertical distance; width (or breadth... In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. ... Mass is a property of a physical object that quantifies the amount of matter it contains. ... Properties The electron is a lightweight fundamental subatomic particle that carries a negative electric charge. ... The term mass in special relativity is used in a couple of different ways, occasionally leading to a great deal of confusion. ... Charge is a word with many different meanings. ... The elementary charge (symbol e or sometimes q) is the electric charge carried by a single proton, or equivalently, the negative of the electric charge carried by a single electron. ... In physics, the electrostatic force is the force arising between static (that is, non-moving) electric charges. ... In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... Gyroscope. ... Plancks constant, denoted h, is a physical constant that is used to describe the sizes of quanta. ... A Hartree (symbol Eh) is the atomic unit of energy and is named after physicist Douglas Hartree. ... In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... A Hartree (symbol Eh) is the atomic unit of energy and is named after physicist Douglas Hartree. ...

Some defined units

Derived Atomic Units
Quantity	Formula	SI Value	Planck unit
time		2.418 884 326 505(16)×10-17 s	10-44 s
Gravitational constant		×1032 m3 kg-1 s-2	1
velocity		2.187 691 2633(73)×106 m s-1	109 m s-1
force		8.238 7225(14)×10-8 N	1044 N
current		6.623 617 82(57)×10-3 A	1025 A
Boltzmann's constant		3×10-6 J K-1	1
temperature		×10-21 K	1032 K

Cover of brochure The International System of Units. ... // In physics, Planck units are physical units of measurement originally proposed by Max Planck. ... A pocket watch. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... The velocity of an object is simply its speed in a particular direction. ... In physics, a force is defined as the rate of change of momentum of that body. ... Look up current in Wiktionary, the free dictionary. ... The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... Temperature is also the name of a song by Sean Paul. ...

Comparison with Planck units

Both Planck units and au are derived from certain fundamental properties of the physical world, and are free of anthropometric considerations. To facilitate comparing the two systems of units, the above tables show the order of magnitude, in SI units, of the Planck unit corresponding to each atomic unit. Generally, when an au unit is "large" in SI terms, the corresponding atomic unit is "small," and vice versa. It should be kept in mind that au were designed for the present day universe, while Planck units are more oriented to cosmology, especially to the state of the universe at the very start of the Big Bang. In physics, Planck units are a system of physical units of measurement. ... It has been suggested that Bertillion Record be merged into this article or section. ... An order of magnitude is the class of scale or magnitude of any amount, where each class contains values of a fixed ratio to the class preceding it. ... Cover of brochure The International System of Units. ... // In physics, Planck units are physical units of measurement originally proposed by Max Planck. ... In physics, Planck units are a system of physical units of measurement. ... // Cosmology, from the Greek: κοσμολογία (cosmologia, κόσμος (cosmos) world + λογια (logia) discourse) is the study of the Universe in its totality, and by extension, humanitys place in it. ... According to the Big Bang theory, the universe emerged from an extremely dense and hot state (bottom). ...

Both au and Planck units normalize the Dirac constant and the Coulomb force constant to 1. Planck units go beyond au mainly by normalizing to 1 the two fundamental constants of general relativity and cosmology: the gravitational constant G and the speed of light in a vacuum, c. Letting α denote the fine structure constant, the au value of c is α^-1 ≈ 137.036. Finally, au normalize a unit of energy to 1, while Planck units normalize to 1 the much better known Boltzmann's constant k. In physics, Planck units are a system of physical units of measurement. ... Plancks constant, denoted h, is a physical constant that is used to describe the sizes of quanta. ... In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ... For a non-technical introduction to the topic, please see Introduction to General relativity. ... // Cosmology, from the Greek: κοσμολογία (cosmologia, κόσμος (cosmos) world + λογια (logia) discourse) is the study of the Universe in its totality, and by extension, humanitys place in it. ... According to the law of universal gravitation, the attractive force between two bodies is proportional to the product of their masses and inversely proportional to the square of the distance between them. ... Cherenkov effect in a swimming pool nuclear reactor. ... The fine-structure constant or Sommerfeld fine-structure constant, usually denoted , is the fundamental physical constant characterizing the strength of the electromagnetic interaction. ... The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ...

au go beyond Planck units by normalizing to 1 the mass and charge of the electron, and a₀, the Bohr radius of the hydrogen atom. Normalizing a₀ to 1 amounts to normalizing the Rydberg constant, R_∞, to 4π/α = 4πc. Given au, the Bohr magneton μ_B=1/2. The corresponding Planck value is e/2m_e. In the Bohr model of the structure of an atom, put forward by Niels Bohr in 1913, electrons orbit a central nucleus. ... A hydrogen atom is an atom of the chemical element hydrogen. ... The Rydberg constant, named after physicist Janne Rydberg, is a physical constant discovered when measuring the spectrum of hydrogen, and building upon results from Anders Jonas Ã…ngström and Johann Balmer. ... In atomic physics, the Bohr magneton (symbol ) is named after the physicist Niels Bohr. ...

au simplify quantum mechanics and electromagnetics

The Schrödinger equation in SI units is: In physics, the Schrödinger equation, proposed by the Austrian physicist Erwin Schrödinger in 1925, describes the time-dependence of quantum mechanical systems. ... Cover of brochure The International System of Units. ...

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The same equation in au is:

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For the special case of the hydrogen atom, the Hamiltonian for its electron, given SI units, is: A hydrogen atom is an atom of the chemical element hydrogen. ... Please wikify (format) this article as suggested in the Guide to layout and the Manual of Style. ... Cover of brochure The International System of Units. ...

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au transforms the preceding equation into:

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Finally, au transform Maxwell's equations into the following elegant form: Maxwells equations (sometimes called the Maxwell equations) are the set of four equations, attributed to James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ...

See also

Planck units In physics, Planck units are a system of physical units of measurement. ...

External links

• CODATA Internationally recommended values of the Fundamental Physical Constants.